M. C. Escher

Based on Wikipedia: M. C. Escher

The Artist Who Made Infinity Visible

Imagine a staircase that climbs forever yet somehow returns to where it started. Or a waterfall that powers a mill wheel, only for the water to flow uphill and cascade down again in an endless loop. These are the impossible worlds of Maurits Cornelis Escher, a Dutch artist who spent his life drawing things that cannot exist—and making you believe, just for a moment, that they could.

Escher died at seventy-three having created some of the most recognizable images in modern art. Yet here's the strange part: the art world largely ignored him for most of his life. He was seventy years old before anyone thought to give him a retrospective exhibition. Critics dismissed his work as too intellectual, too mathematical, insufficiently emotional. It wasn't until scientists and mathematicians embraced him—and until his images started appearing on college dorm room walls, album covers, and the pages of Scientific American—that the rest of the world caught on.

This is the story of a man who failed the second grade, couldn't pass his architecture exams, and claimed to have no mathematical ability whatsoever. He just happened to discover, in the geometric patterns of a medieval Spanish palace, a visual language that would obsess him for the rest of his life.

A Sickly Boy Who Could Draw

Escher was born on June 17, 1898, in the Dutch city of Leeuwarden, in a house that today serves as a ceramics museum. His father was a civil engineer, and young Maurits—called "Mauk" by family and friends—was the youngest son. He was a weak, sickly child who spent time in a special school and struggled academically. His grades were poor across the board.

Except for drawing. At that, he excelled.

When he was thirteen, his carpentry and piano lessons ended. At twenty, he enrolled at the Technical College of Delft, then moved on to the Haarlem School of Architecture and Decorative Arts. He tried architecture but failed several subjects, partly because of a persistent skin infection, and switched to decorative arts. His teacher there was a graphic artist named Samuel Jessurun de Mesquita, who would have a profound influence on his development.

But the real education came when Escher left the classroom entirely.

The Alhambra Revelation

In 1922, at twenty-four years old, Escher traveled through Italy and Spain. He visited Florence, Siena, Toledo, Madrid. The Italian countryside charmed him—its hills and ancient towns would appear in his work for years to come. But it was in Granada, in southern Spain, that something clicked.

The Alhambra is a palace and fortress complex built by Moorish rulers in the fourteenth century. Its walls and ceilings are covered with intricate geometric patterns: interlocking shapes that repeat endlessly across surfaces, filling every available space without gaps or overlaps. Islamic art, which traditionally avoided representational imagery, had developed these geometric designs—called tessellations—to an extraordinary degree of sophistication.

Escher was transfixed.

A tessellation is simply a pattern of shapes that tile a surface perfectly. Think of a bathroom floor: the tiles fit together with no gaps between them. But the Alhambra's patterns weren't just squares or hexagons. They were complex interlocking forms, each shape fitting precisely into its neighbors like pieces of an infinite puzzle.

Escher returned to Spain in 1936, spending days at a time sketching the Alhambra's patterns in painstaking detail. He later described his fascination as an addiction:

It remains an extremely absorbing activity, a real mania to which I have become addicted, and from which I sometimes find it hard to tear myself away.

This was the pivotal moment. Before the Alhambra, Escher drew what he saw: landscapes, buildings, insects, plants. After the Alhambra, he began drawing what he imagined—impossible worlds built from mathematical principles he couldn't quite name but could intuitively grasp.

Mathematics Without Knowing It

Here's what makes Escher's story remarkable: he genuinely believed he had no mathematical ability. He'd failed subjects in school. He couldn't do advanced calculations. Yet the work he produced was so mathematically sophisticated that crystallographers and geometers studied it with the same intensity they brought to their own research.

His brother Berend, a geologist, sent him papers by the mathematician George Pólya and the crystallographer Friedrich Haag on something called plane symmetry groups. These are the mathematical rules that govern how patterns can repeat across a flat surface. There are exactly seventeen different ways to tile a plane with repeating patterns—not sixteen, not eighteen, but precisely seventeen. Mathematicians had proven this.

Escher studied all seventeen. Then he created his own drawings exploring each type of symmetry, developing his own notation system to track what he was doing. He filled a sketchbook with methodical investigations that one mathematician later described, without qualification, as genuine mathematical research.

The questions Escher was asking himself were sophisticated ones: What shapes can tile a plane perfectly? How must the edges of such shapes relate to each other? He wasn't solving these problems with equations—he was solving them with pencil and paper, through trial and error and visual intuition.

His tessellations evolved beyond the geometric abstractions of the Alhambra. Instead of interlocking stars and polygons, Escher created interlocking birds, fish, lizards, and angels. In his 1943 lithograph Reptiles, green, red, and white lizards crawl across a page, their heads meeting at vertices, their tails and legs fitting together with jigsaw precision. Look at it long enough and you realize: every lizard is identical, just rotated or flipped, and together they fill the entire surface with no gaps.

The Impossible Becomes Visible

Tessellations were only the beginning. As Escher's confidence grew, he began exploring something even stranger: objects and spaces that look coherent at first glance but cannot actually exist in three dimensions.

Consider a staircase. In reality, if you climb stairs continuously in one direction, you end up higher than where you started. That's what stairs do. But Escher's 1960 lithograph Ascending and Descending shows a rectangular building with a staircase running around its roof. Monks trudge up the stairs in an endless procession—except the staircase somehow loops back on itself. Climb forever and you return to where you began, having neither ascended nor descended.

This particular optical illusion has a name: the Penrose stairs, after the mathematician Roger Penrose and his father Lionel Penrose, a biologist. In 1956, they published a paper titled "Impossible Objects: A Special Type of Visual Illusion," which described several structures that appear valid when drawn but cannot be constructed in physical space. They sent Escher a copy.

Escher wrote back with enthusiasm, enclosing a print of the very work their paper had inspired.

The Penroses also described the tribar, sometimes called the Penrose triangle: three bars that appear to connect at right angles, forming a triangle—except if you trace the bars with your finger, you realize the geometry is impossible. Escher used this shape repeatedly in his 1961 lithograph Waterfall, which depicts a water channel that somehow flows uphill to power a waterwheel, then falls down to begin the cycle again. It's a perpetual motion machine that works only on paper.

What makes these images so compelling is that they're not abstract. Escher populated his impossible architecture with people going about their business: climbing stairs, carrying baskets, contemplating the view. The impossibility becomes more disturbing because everyone in the picture treats it as normal.

Infinity in a Frame

Escher was haunted by infinity. How do you represent something endless within the finite boundaries of a picture?

One approach he developed was the use of repeating patterns that shrink toward the edges of a circle. His 1969 woodcut Snakes—the last piece he ever completed—shows rings linked together in an endless chain, with snakes winding through them. As your eye moves from the center toward the edge (or from the edge toward the center), the rings become smaller and smaller, approaching but never quite reaching an infinitely small size.

This wasn't just artistic intuition. Escher had corresponded with the mathematician Donald Coxeter, who worked on hyperbolic geometry—a type of non-Euclidean geometry where the normal rules of parallel lines don't apply. Coxeter's diagrams showed how patterns could tile hyperbolic space, with shapes shrinking infinitely toward a circular boundary. Escher adapted these mathematical insights into some of his most celebrated works.

Snakes was exceptionally difficult to produce. Woodcuts require carving the image in reverse onto a wooden block, then applying ink and pressing paper against it. For Snakes, Escher used three separate blocks, each printed three times by rotating it around the center of the image—nine printing operations total, all requiring precise alignment to avoid gaps or overlaps. A video recording of Escher at work on this piece shows the meticulous care he brought to the process.

He finished it in July 1969. He was seventy-one years old and would live only three more years. In this final work, you can see everything that defined his art: symmetry, interlocking patterns, and the representation of infinity within finite bounds.

A Life Shaped by Movement

Escher's personal life was marked by displacement. After marrying Jetta Umiker, a Swiss woman he met in Italy, he settled in Rome in 1923. They had three sons: Giorgio, Arthur, and Jan. For over a decade, Escher explored the Italian landscape, traveling frequently and sketching the hill towns and coastlines that would populate his early work.

But by 1935, Fascism under Mussolini made Italy intolerable. Escher had no interest in politics—he once said he found it impossible to involve himself with any ideals other than expressing his own concepts through his own medium. Yet he was repulsed by fanaticism and hypocrisy. When his eldest son was forced to wear a Ballila uniform (the youth organization of the Fascist party) at age nine, the family left.

They moved to Switzerland, but Escher was miserable there. He had loved the Italian light, the ancient architecture, the dramatic landscapes. Switzerland felt cold and gray. After two years, they relocated to a suburb of Brussels, Belgium. Then the Second World War began, and in January 1941, they moved again, this time to Baarn in the Netherlands.

Escher would live in Baarn for nearly thirty years. Ironically, it was in the cloudy, wet Dutch weather—so unlike the Mediterranean landscapes he loved—that he produced most of his greatest work. The gloomy climate, he found, allowed him to focus intensely on his studio practice. Without the temptation to go outside and sketch from nature, he turned inward, toward the mathematical visions that now consumed him.

Recognition Deferred

For decades, the art establishment didn't quite know what to do with Escher. His technical skill was undeniable—he was a master printmaker who worked in woodcut, lithograph, and mezzotint with equal facility. But his subjects seemed too cold, too cerebral. Art critics wanted emotion, spontaneity, the hand of the artist visible in every brushstroke. Escher gave them precision, planning, and mathematical rigor.

It didn't help that his work resisted easy categorization. He shared something with the Surrealists—particularly René Magritte, who also painted images that defied logical interpretation. He anticipated Op Art, which explored optical illusions and perceptual tricks. But Escher kept his distance from movements and manifestos. He worked alone, following his own obsessions.

The breakthrough came from an unexpected direction: the scientific community. Crystallographers recognized the mathematical sophistication in his tessellations. Mathematicians saw in his impossible objects a playful exploration of logical paradoxes. And in April 1966, the popular mathematics writer Martin Gardner devoted his "Mathematical Games" column in Scientific American to Escher's work.

This was enormous. Scientific American had a readership of educated professionals—doctors, engineers, scientists—who might never visit an art gallery but who found Escher's images thrilling. His work started appearing on textbook covers, on album art, on the walls of college dormitories. A popular audience had discovered him, even as galleries continued to keep their distance.

The ultimate tribute came in 1979, when Douglas Hofstadter published Gödel, Escher, Bach: An Eternal Golden Braid. The book, which won the Pulitzer Prize, explored the connections between the mathematical logician Kurt Gödel, the composer Johann Sebastian Bach, and Escher. Hofstadter saw in all three a fascination with self-reference and strange loops—systems that fold back on themselves in impossible ways. The book made Escher a household name among intellectuals who might never have encountered his work otherwise.

The Predecessors He Admired

Escher wasn't working in a vacuum. He knew he had forerunners, artists who had explored similar territory centuries before.

One was Giovanni Battista Piranesi, an eighteenth-century Italian artist known for a series of prints called the Carceri—"Prisons." These dark, fantastical images depict vast architectural spaces filled with staircases, ramps, bridges, and arches that seem to go nowhere. Tiny human figures wander through these impossible structures. Escher kept several Piranesi prints in his studio.

Another predecessor was the Renaissance painter Parmigianino, who in 1524 created a self-portrait using a convex mirror. The curved surface distorted his hand in the foreground while his face receded into the distance—an early exploration of non-Euclidean geometry in art. William Hogarth, the eighteenth-century English satirist, had also played with impossible perspectives in his 1754 print Satire on False Perspective, which deliberately includes every perspective error an artist could make.

Escher was aware of these precedents and drew energy from them. But where earlier artists had treated optical paradoxes as curiosities or jokes, Escher made them central to his vision. He didn't want to satirize perspective—he wanted to show you what lay beyond it.

Final Years

In 1970, Escher moved to the Rosa Spier Huis in Laren, a retirement home for artists where he had his own studio. He was in declining health but continued to work when he could. He died in a hospital in Hilversum on March 27, 1972, and was buried at the New Cemetery in Baarn.

His legacy was still taking shape. In the decades after his death, major exhibitions traveled the world. Museums that had once ignored him now competed to display his work. The art world's attitude shifted—not because critics suddenly developed a taste for mathematical imagery, but because Escher's popular success was simply too significant to ignore. When millions of people recognize your images, when your work illustrates concepts in fields from physics to computer science, the question of whether you're a "real artist" becomes somewhat academic.

Escher himself remained modest about his abilities. He insisted he wasn't a mathematician, despite the evidence of his notebooks. He described himself as a "reality enthusiast"—someone fascinated by the nature of space and perception, who happened to express that fascination through images that obeyed rules no reality could follow.

Perhaps that's the key to his enduring appeal. Escher didn't ask you to understand mathematics. He asked you to look at a staircase that climbs forever, or a hand drawing itself into existence, or a waterfall that defies gravity—and wonder, just for a moment, whether the impossible might be real after all.